Weight distribution for non-binary cluster LDPC code ensemble

In this paper, we derive the average weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we give the exponential growth rate of the average weight distribution in the limit of large code length. We show that there exist (2, d_c)-regular non-binary cluster LDPC code ensembles whose normalized typical minimum distances are strictly positive.